Here are some articles (history.state.gov and umich.edu) talking about the US push to dissolve the imperial preference system. In the conferences that occurred during WW2 the US told Britain explicitly that they must dissolve the imperial preference system. From here can one construct an argument that the financial burden the empire, without the benefit of its imperial preference all but guaranteed the end of the British empire.
Would argue it is other way around
Imperial Preference is simply another tariff system enacted by country to protect its own producers from competition abroad. You slap tariffs on imported goods, they become more expensive and less competitive on your market. Down side of this is that usually countries affected by this respond in kind, putting tariffs on goods coming from your country.
As with any government measure, there were winners and there were losers. British Empire was structured as usual colonial empire from that era, with mainland having much more developed industry then colonies. Colonies on the other hand supplied mainland with raw materials, foodstuff etc… Imperial Preference arguably protected industry and had little to no benefit for let's say agricultural producers in colonies. For example British automotive industry benefited from tariffs that hampered their competition in US (and Germany before the war) . However, mango producers in India perhaps even suffered as a consequence of retaliatory tariffs that made their goods more expensive abroad.
Independence movements in colonies existed long before WW2, and they recognized that tariffs and whole economic system are not beneficial to the population of colonies. One famous example is Gandhi's rejection of European clothing (mostly produced outside of India) and his general attitude that Indians should reject British products, part of Swadeshi Movement.
Atlantic conference happened in August of 1941. No matter how we judge US request concerning Imperial Preference and other things (altruistic or merely wanting to open another huge market for US products) , by that time it was already too late for British Empire in present form. In India, beside pacifist Gandhi there were much more radical leaders like Bose who were prepared to work even with Axis to force India's independence. Already in 1942 , British wanted negotiations about future status of India with much more autonomy going to full independence. Since India was jewel in the crown of British Empire, with India going it could be expected that British possession in Middle East and Africa would follow suit .
As a conclusion, it could be argued that uneven economic status and development strengthened anti-colonial and centrifugal forces. By the time Atlantic Charter it was too late to salvage things. US requests simply confirmed to British that sun is finally setting on their empire.